How about writing a batch file to distribute to a list of recipients and then the teach just has to drop a file on the icon?
If these are just files, as opposed to executables, you could create a series of read-only shared folders which could be mapped to a desktop shortcut called something like "Class Materials." Once set up, you could then have the students open the folder (under a teacher's direction) and drag/copy any enclosed files onto the individual desktops. It's just like having the students get a book off the shelf and bring it back to their desks.
Access to specific folders could be controlled through the usual group/folder share privileges so the 8th graders wouldn't be loading shortcuts meant for the 12th graders, etc, or deleting or adding their own stuff to the folders.
You could even structure it in such a way that the individual teachers have read/write/delete access to these folders thereby allowing them distribution control over any files needed for their courses. These desktop folders could also be synchronized to the desktop from the server. Just be sure to set the override option to force the desktops to synchronize from
the server folder only. Don't do a 2-way sync or you'll have major problems.
We set up a version of this for a school once. It worked out very well for them.
There's always 'push server' (SMS et al) solutions for more complex deployments. But they can be quite expensive. They're also fairly complex to set up and administer. So, if you're uncomfortable with batch commands, something like SMS definitely is going to be out of the question.